I suppose the meta-question is: Where do I read about this? Engineering major, not physics. Worked through Penrose's book until the tensor calculus on manifolds chapter and then sank without a trace. The popularized descriptions of quantum physics are hopelessly incomplete and as Feynman...
Thecla, interesting that you mention 24 hours. The original Scientific American article appeared in the 80's and did not show any moves but discussed the cube in terms of groups and operators. It took me three days, no more than 8 hours a day, to discover operators that would swap edge cubes...